1: The concept of a singularity was born in obscure areas of pure mathematics, precisely in “topology”. Singularities are involved in self-organizing processes at many different physical scales and levels of complexity. At the first level, the level of physics, there are phase transitions in non-organic matter. At the level of chemistry, we find singularities triggering the spontaneous assembly of chemical clocks —chemical reactions in which billions of molecules suddenly begin to oscillate coherently—
2: “the turbulent behaviour of liquids, for example, with its exquisite structure of nested vortices and eddies, each contained in or containing the next, has come to be seen as a wonderfully ordered process. But as the previous quote indicates, more important than turbulent behaviour itself is that special, singular moment at the onset of turbulence. A liquid sitting still or moving at a slow speed is in a relatively disordered state: its component molecules move aimlessly, bumping into each other at random. But when a certain threshold of speed is reached, a flowing liquid undergoes a process of self-organization: its component molecules begin to move in concert to produce highly intricate patterns. Transition points like these, called “singularities,” where order spontaneously emerges out of chaos, have been the subject of intense scientific analysis over the last three decades. These points or thresholds in the rate of flow of matter and energy are referred to as “singular” because they are rare and special.” (DeLanda M., “War in the Age of Intelligent Machines”, p. 15., 1991) Thus empirical evidence, it may be said that in the surroundings of a singularity a set of previously disconnected elements converges into a synergistic whole. There is almost no evidence that the singularities themselves play a causal role in this process. 
(luis fernando odiaga, 26/11/07)
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